how can i get the resonance frequency for a damped system? x'' + 2r x' + w. x = F/m coswt r is the damping factor, w. the natural frequency it can be calculated that the amplitude, A=F/m / sqrt( (w.^2-w^2)^2-(2rw)^2) by differentiating wrt w, it is found the maximum amplitude occurs at w=sqrt(w.^2-2r^2) is this the resonance frequency? or should i look at the frequency w=sqrt(w.^2-r^2), which is the frequency of the transient solution when the system is not forced. is the solution at this frequency unbounded? in the form x=Bt cos (sqrt(w.^2-r^2))t so which is resonance frequency? w=sqrt(w.^2-2r^2) or w=sqrt(w.^2-r^2) ??